subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | How many multiples of 2 are there between 1 and 58, exclusive? | [
"21",
"22",
"24",
"26",
"28"
] | 28
multiples of 2 between 1 and 58 exclusive.
from 2 * 1 upto 2*28, (1,2,3,4,...,28). Hence, 28 multiples !
correct option is E
The answer is: E | E |
mathematics | Annie and Sam set out together on bicycles traveling at 15 and 12 km per hour respectively. After 40 minutes, Annie stops to fix a flat tire. If it takes Annie 25 minutes to fix the flat tire and Sam continues to ride during this time, how many minutes will it take Annie to catch up with Sam assuming that Annie resumes... | [
"20",
"40",
"60",
"80",
"100"
] | Annie gains 3 km per hour (or 1 km every 20 minutes) on Sam.
After 40 minutes Annie is 2 km ahead.
Sam rides 1 km every 5 minutes.
In the next 25 minutes, Sam rides 5 km so Sam will be 3 km ahead.
It will take Annie 60 minutes to catch Sam.
The answer is C.
The answer is: C | C |
mathematics | A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red? | [
"24/455",
"3/91",
"12/455",
"15/91",
"None of these"
] | Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13) = 12/455
ANSWER:C
The answer is: C | C |
mathematics | There are 12 intermediate stations between two places A and B. Find the number of ways in which a train can be made to stop at 4 of these intermediate stations so that no two stopping stations are consecutive? | [
"108",
"112",
"126",
"140",
"None of these"
] | Explanation :
Initially, let's remove the 4 stopping stations
Then we are left with 8 non-stopping stations (=12-4) as shown below
(non-stopping stations are marked as 1,2 ... 8)
Now there are 9 positions (as marked by * in the above figure) to place the 4 stopping stations
such that no two stopping stations are consec... | C |
mathematics | Five pieces of wood have an average length of 120cm and a median length of 140cm. What is the maximum possible length, in cm, of the shortest piece of wood? | [
"a) 90",
"b) 100",
"c) 110",
"d) 130",
"e) 140"
] | A. 90
sum of all lengths of all 5 pieces of wood = 124 * 5 = 600
3rd piece (sorted in increasing length) length = 140 (median)
for sum of first 2 wood length to become max, last two should be least.
let 4th, 5th wood also have length 140 each.
total of last 3 = 140 * 3 = 420
sum of first 2 = 600 - 420 = 180
each of the... | A |
mathematics | An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of: | [
"150",
"720",
"160",
"80",
"12"
] | Explanation:
Speed = Distance/Time
Speed =1200(5/3)km/hr
Required speed =(1200*(3/5))km/hr=720 km/hr
Answer B
The answer is: B | B |
mathematics | A grocer buys apples for 81¢ per pound. If 10% of the apples goes bad and he still wants to make a 20% profit over his purchase price, what should be the sales price? | [
"100¢",
"108¢",
"110¢",
"95¢",
"99¢"
] | for making calculation simple let us consider he buys 10pounds @ 81/pound=810¢ in total .
10% apples lost...means 9 pounds left.
further he wants 20% profit on 810 ¢
means he wants to earn 972¢
sales price should be 972/9=¢ 108
Ans B
The answer is: B | B |
mathematics | Bruno and Sacha are running in the same direction around a stadium. Sacha runs at a constant speed of 6 meters per second, and Bruno runs at a constant speed of 5 meters per second. At a certain point Sacha overtakes Bruno. If three minute afterward, Sacha stops and waits for Bruno to reach him, then how many seconds d... | [
"12",
"24",
"36",
"60",
"72"
] | the difference of the speed is 1m per second so in three minute Sacha will be 180 m ahead of Bruno..
Bruno will cover this in 180/5=36 secs..
C
The answer is: C | C |
mathematics | A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16? | [
"1/6",
"7/216",
"1/36",
"9/216",
"11/216"
] | the total number of possible outcomes is, of course, 6^3.
Fortunately, there are only two combinations of three dice throws that will give you a sum of 16:
5, 5, 6
4, 6, 6
(I have a hard time remembering a real GMAT question that would give you 12, as the number of potential combinations is indeed inordinately large an... | C |
mathematics | Two goods train each 500 m long are running in opposite directions so parallel tracks.Their speeds are 45 kmph and 30 kmph respectively.Find the time taken by the slower train to pass the driver of the first one | [
"12 sec",
"24 sec",
"48 sec",
"60 sec",
"65 sec"
] | only need length of slower train which is L=500m
relative sped (both are opposite direction)
s=45+30=75kmph
75*5/18=125/6 m/s
time =dist/speed
=(500*6)/125=24 sec
ANSWER:B
The answer is: B | B |
mathematics | Find the length of the wire required to go 15 times round a square field containing 69696 m2? | [
"15840",
"19879",
"27997",
"15842",
"15823"
] | a2 = 69696 => a = 264
4a = 1056
1056 * 15
=15840
Answer:A
The answer is: A | A |
mathematics | In a match, awards are given to each of 11 members of the team and a trophy to the team. In all winning team gets 2.75kg weight awards. If the weight of match wining trophy is 1.275kg, what the weight of each player giving weight of trophy ? | [
"134.09 gms",
"144.09 gms",
"154.09 gms",
"164.09 gms",
"174.09 gms"
] | Total weight of all the awards for winning team is 2.75kg = 2750gms
trophy weight is 1.275 kg=1275gms
now rest weight = 2750-1275= 1475gms
rest weight divided in 11 players is = 1475/11 = 134.09 gms
ANSWER:A
The answer is: A | A |
mathematics | In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done? | [
"6^6 ways",
"8^9 ways",
"7^8 ways",
"8^7 ways",
"8^6 ways"
] | 6 people can be prized with distinct prizes in 6^6 ways
ANSWER:A
The answer is: A | A |
mathematics | 18 chess players take part in a tournament. Every player plays twice with each of his opponents. How many games are to be played? | [
"230",
"274",
"306",
"354",
"424"
] | 2*18C2 = 2*153 = 306
The answer is C.
The answer is: C | C |
mathematics | Which number is the odd one out in the list ? | [
"38442",
"78426",
"84029",
"67626",
"72927"
] | C
84029
All the others are three digit numbers followed by their square root, eg 729 followed by its square root, 27.
Answer: C
The answer is: C | C |
mathematics | The average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students? | [
"52.6",
"52.4",
"52.1",
"52.5",
"52.9"
] | Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80 = 52.5.Answer: D
The answer is: D | D |
mathematics | Which of the following inequalities is equivalent to 40 + 6x > -3x - 11x + 20? | [
"x < 1",
"x < -1",
"x < 3",
"x < -3",
"x < 4"
] | You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide ... | D |
mathematics | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? | [
"278",
"279",
"999",
"287",
"287"
] | a2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5
= 999
Answer:C
The answer is: C | C |
mathematics | Ashley paid 5 dollars for 1 notebook and 1 pencil. If both prices were integers, how many pencils did Ashley buy if she paid 93 dollars for the pencils and for 15 notebooks? | [
"6.",
"16.",
"18",
"21",
"26"
] | 5 = 1P + 1 N
93 = XP + 15N, where X is the number of pencils
Possible prices for 1P & 1N (integers):
N = 1 P = 4 then 15N = 15, 4X = 93 - 15 = 78, X = 19.5 (not an integer)
N = 2 P = 3 then 15N = 30, 3X = 93 - 30 = 63, X = 21 (the answer we were looking for, no need to continue calculations)
N = 3 P = 2
N = 4 P =1
Answ... | D |
mathematics | Robert is traveling from one end of a forest to the other. In order to find his way back, he is leaving morsels of bread in the following pattern: 2 morsels of milk, 3 morsels of white, and 1 morsel of rye. The pattern repeats after he leaves the morsel of rye. If Robert drops 2,000 morsels of bread, what are the last ... | [
"rye − milk − milk",
"milk − milk − white",
"white − rye − milk",
"white − white − white",
"white − white − rye"
] | In a single round Robert drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of milk --> Options B, C, D and E can be eliminated
Answer: A
The answer is: A | A |
mathematics | Share Rs.4200 among John, Jose & Binoy in the ration 2 : 4 : 6.Find the amount received by John? | [
"900",
"980",
"1200",
"1240",
"1400"
] | Amount received by sanjay.
4 / 12 X 4200 = 1400= ( related ratio / sum of ratio ) x Total amount
So, the Amount received by sanjay is 1400.
E
The answer is: E | E |
mathematics | A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? | [
"40%.",
"60%.",
"80%.",
"100%.",
"120%."
] | 20% of 30 = 6 rupee profit
36/3 = 12 rupee per passenger
12*4 = 48
48 - 24 = 24.
so profit = 100%.
ANSWER:D
The answer is: D | D |
mathematics | The Coen family consists of a father, a mother, two children and a dog. A photographer is about to take the family's picture. How many different arrangements (of standing in a row) does the photographer have, if it is known that the father insists of standing by his first child? | [
"12",
"24",
"30",
"48",
"120"
] | We need to find the number of arrangements of Father, Mother, Child-1, Child-2, and a Dog, so that F and C1 are always together.
Consider F and C1 to be one unit, then we would have total of four units: {FC1}, {M}, {C2}, {D}. The number of arrangements of these four units is 4!, but F and C1 within their unit can be ar... | D |
mathematics | The radius of a cone is 8 m, height 6 m. Find the slant height? | [
"5",
"10",
"15",
"20",
"25"
] | Cone slant height (l) = √r(power2)+h(power2)
= √64+36 = 10 m.
Answer is B.
The answer is: B | B |
mathematics | Find the odd man out. 2, 3, 5, 9, 12, 17, 23 | [
"12",
"9",
"23",
"2",
"3"
] | Explanation :
2
2 + 1 = 3
3 + 2 = 5
5 + 3 = 8
8 + 4 = 12
12 + 5 = 17
17 + 6 = 23
ie, 8 should have come in place of 9
Answer : Option B
The answer is: B | B |
mathematics | Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are | [
"4, 8, 12",
"5, 10, 15",
"10, 20, 30",
"12, 24, 36",
"None of these"
] | Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12
The numbers are 12, 24, 36. Answer: D
The answer is: D | D |
mathematics | Spandy travels from X to Y at a speed od 40 kmph and returns by increasing his speed by 50%. What is his average speed for the whole journey? | [
"36 kmph",
"45 kmph",
"48 kmps",
"45 kmps",
"42 kmps"
] | Explanation :
Let the distance between X and Y be x km.
Time taken from X to Y @ 40 km/h=(x/40)hours
Time taken from Y to X @ 60 km/h=(x/60)hours
Average speed=2x/((x/40)+(x/60))= 48 km/h.
Answer : C
The answer is: C | C |
mathematics | The difference between the compound interest and simple interest on a certain sum at 20% per annum for 2years is $500. Find the sum? | [
"$10000",
"$50000",
"$15200",
"$12500",
"$15000"
] | Let the sum be $x
C.I. = x(1+20/100)^2 - x = 35x/100
S.I. = (X*20*2)/100 = 2x/5
C.I.- S.I. = (35x/100)-(2x/5) = 5x/100
5x/100 = 500
x = 10000
Answer is A
The answer is: A | A |
mathematics | An inspector rejects 0.08% of the meters as defective, How many meters he examine to reject 2 meteres | [
"1300",
"1400",
"2400",
"2500",
"2600"
] | It means that 0.08% of x = 2
(8100×100 ×x)=2
x=2×100×1008
x=2500
ANSWER :D
The answer is: D | D |
mathematics | Nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw. If the total weight of one screw and one nail is half that of 6 screws and one nail, then the total weight of 3 screws, and 3 nails is how many times that of 2 screws and 4 nails? | [
"a. 4",
"b. 5/2",
"c. 2",
"d. 3/2",
"e. 5/4"
] | let the weight of nail be n and that of screw be s..
so s+w=1/2 * (6s+1n)...
or 1n = 4s..
lets see the weight of 3 s and 3n= 3s+3*4s=15s..
and weight of 2s and 4n= 2s+4*2s=10s..
ratio= 15s/10s=15/10=3/2
D
The answer is: D | D |
mathematics | The age of man is three times the sum of the ages of his two sons. Eight years hence,his age will be double of the sum of the ages of his sons.The father’s present age is : | [
"40 years",
"45 years",
"50 years",
"55 years",
"72 years"
] | Solution
Let the sum of present ages of the two sons be x years.
Then,father's present age = 3x years.
∴ (3x + 8)=2 (x +16) ⇔ 3x + 8 = 2x + 32 ⇔ x =24.
Hence,father's present age = 72 years. Answer E
The answer is: E | E |
mathematics | Three numbers are in the ratio 5 : 6 : 7. The sum of its longest and smallest numbers equals the sum of the third number and 48. Find the third number? | [
"18",
"76",
"48",
"27",
"12"
] | Let the numbers be 5x, 6x, 7x.
Largest number = 7x.
Smallest number = 5x.
Third number = 6x.
7x + 5x = 6x + 48
6x = 48 => third number is 48.
Answer:C
The answer is: C | C |
mathematics | One cutting machine cuts 100 metal bars in 30 minutes.Another machine does the same job in 30 seconds.What time will it take if both machines are put on the same work ? | [
"25.0 seconds",
"29.5 seconds",
"30.0 seconds",
"30.5 seconds",
"30.7 seconds"
] | By guess it is clear that the time taken will be less than 30 seconds and very near to it. Therefore, answer 29.5 seconds will be correct. Answer-B
The answer is: B | B |
mathematics | The average (arithmetic mean) of four different positive integers is 15. If the first of these integers in 3 times the second integer and the second integer is 2 less than the third integer, what is the least possible value of the fourth integer? | [
"8",
"4",
"3",
"2",
"1"
] | Let the second integer be x and the fourth be a.
Then [3x + x + (x+2) + a]/4 =15
=> 5x + 2 + a = 60
=> 5x + a = 58
=> a = 58 - 5x
From the above equation we can see that a is minimum when x is maximum, provided both are positive
The maximum value that x can take in the above equation while still keeping a positive is x... | A |
mathematics | 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points? | [
"334",
"377",
"495",
"766",
"261"
] | Explanation:
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is \inline {\color{Black}12C_4{}} = 495.
Therefore, we can draw 495 quadrilaterals
Answer: C) 495
The answer is: C | C |
mathematics | A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 20 years now, the son's age five years back was: | [
"9 years.",
"8 years.",
"7 years.",
"5 years.",
"6 years."
] | Let the son's present age be x years. Then, (20- x) = x
2x = 20
x = 10.
Son's age 5 years back (10 - 5) = 5 years.
Answer: Option D
The answer is: D | D |
mathematics | A candidate got 32% of the votes polled and he lost to his rival by 1908 votes. How many votes were cast? | [
"5100",
"5200",
"5300",
"5400",
"5500"
] | Let x be the total number of votes.
0.32x + 1908 = 0.68x
0.36x = 1908
x = 1908/0.36 = 5300
The answer is C.
The answer is: C | C |
mathematics | Mixture A is 30 percent alcohol, and mixture B is 60 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 40 percent alcohol, approximately how many gallons of mixture A are in the mixture? | [
"0.8",
"0.7",
"0.6",
"0.5",
"0.4"
] | (60-50)/(50-30) = Qa/Qb
10/20= Qa/Qb
1/2 = Qa/Qb
Qa = (1/6) * 4 = 4/6 = 1/2 = 0.50
Answer : D
The answer is: D | D |
mathematics | In a fuel station the service costs $2.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars? | [
"320$",
"380$",
"420$",
"450$",
"462$"
] | 12*2.75 + 0.65*12*55 = 462 hence - E
The answer is: E | E |
mathematics | Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.55%, what fraction of the products was che... | [
"1/3",
"1/4",
"1/5",
"1/6",
"1/8"
] | x: 0.5% is 0.05%-points from 0.55%.
y: 0.8% is 0.25%-points from 0.55%.
Therefore the ratio of products checked by y:x is 1:5.
Thus, worker y checked 1/6 of the products.
The answer is D.
The answer is: D | D |
mathematics | A man rides at the rate of 20km/hr. But stops 10minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 175 kilometers? | [
"9hr",
"8 hr 30 min",
"9hr 45min",
"6hr 20min",
"8hr 40min"
] | speed of man = 20km/hr
number of rests = (175/25)-1 = 6
time taken for the man = (175/20)+6*(10/60) = 9 hr 45 min
Answer is C
The answer is: C | C |
mathematics | If G is a negative integer, which of the following must be a negative integer? | [
"G + 1",
"G/2+3",
"G^4",
"G – y",
"G^11"
] | We need to check each option here:
A. G + 1
This will depend on the value of G. Nothing can be said
B. G/2+3
This will depend on the value of G. Nothing can be said
C. G^4
This will always be positive. Even powers of negative numbers are positive and odd powers are negative
D. G – y
This will depend on the value of G. ... | E |
mathematics | Sakshi can do a piece of work in 20 days .Tanya is 25% more efficient than Sakshi. the number of days taken by tanya to do the same piece of work is? | [
"25days",
"45days",
"24days",
"16days",
"36days"
] | The ratio of times taken by Sakshi and Tanya=125:100=5:4.
suppose Tanya takes x days to do the work.
5:4::20:x
x=(4*20)/5
x=16 days
Tanya can do work in 16 days
Answer(D)
The answer is: D | D |
mathematics | For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 940, what i... | [
"24",
"22",
"16",
"18",
"20"
] | we know that : x > 1, y > 1, and x + 3y < 940,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest noall factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 ... | C |
mathematics | If a committee of 4 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many such committees are possible? | [
"20",
"40",
"50",
"80",
"120"
] | Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 4 couples (as there should be 4 members) each to send onerepresentativeto the committee: 5C4=5.
But these 4 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=40.
Answer... | B |
mathematics | In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes? | [
"5 C 3",
"5 P 3",
"5(3)",
"3(5)",
"2(5)"
] | Explanatory Answer
Sampling with replacement
The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any n... | D |
mathematics | How many multiples of 5 are there between 5 to 100? | [
"9",
"18",
"17",
"none of these",
"Cannot be determined"
] | Explanation :
As you know, multiples of 5 are integers having 0 or 5 in the digit to the extreme right (i.e. the units place).
So the numbers are 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95.
Answer : B
The answer is: B | B |
mathematics | A can complete a work in 12days and B can do the same work in 6days. If A after doing 3days, leaves the work, find in how many days B will do the remaining work? | [
"2 1/2days",
"4 1/2days",
"6 1/2days",
"7 1/2days",
"10 1/2days"
] | The required answer = (12-3)*6 / 12 = 54/12 = 4 1/2days
Answer is B
The answer is: B | B |
mathematics | The average weight of 5 person's increases by 10.0 kg when a new person comes in place of one of them weighing 40 kg. What might be the weight of the new person? | [
"76 kg",
"76.5 kg",
"90 kg",
"Data inadequate",
"None of these"
] | Explanation:
Total weight increased = (5 x 10.00) kg = 50 kg.
Weight of new person = (40 + 50) kg = 90 kg.
Answer: C
The answer is: C | C |
mathematics | The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the width of this rectangle. | [
"W = 27",
"W = 15",
"W = 38",
"W =43",
"W = 13"
] | L * W = 300 : area , L is the length and W is the width.
2 L + 2 W = 70 : perimeter
L = 35 - w : solve for L
(35 - W) * W = 300 : substitute in the area equation
W = 15 and L = 20 : solve for W and find L using L = 35 - w.
correct answer B
The answer is: B | B |
mathematics | What percent of a day is six hours? | [
"20.83%",
"25%",
"18x2/3%",
"22x1/2%",
"None of these"
] | Explanation :
Required percentage = (6/24100)%
= 25%.
Answer : B
The answer is: B | B |
mathematics | How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm? | [
"6400",
"6410",
"6440",
"6500",
"6800"
] | Number of bricks = Volume of Wall/Volume of Bricks
=800x600x22.5/21x11.25x6= = 6400
answer :A
The answer is: A | A |
mathematics | Eddy and Freddy start simultaneously from city A and they travel to City B and City C respectively. Eddy takes 3 hours and Freddy takes 4 hours to complete the journey. If the distance between City A and City B is 450 kms and City A and City C is 300 kms. What is the ratio of their average speed of travel? (Eddy: Fredd... | [
"8/3",
"2/1",
"8/5",
"5/8",
"5/3"
] | Distance traveled by Eddy = 600 km
Time taken by Eddy = 3 hours
Average speed of Eddy = 450/3 = 150 km/hour
Distance traveled by Freddy = 300 km
Time taken by Freddy = 4 hours
Average speed of Freddy = 300/4 = 75 km/hour
Ratio of average speed of Eddy to Freddy = 150/75 = 2/1
Answer B
The answer is: B | B |
mathematics | A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | [
"50 Kmph",
"60 Kmph",
"65 Kmph",
"70 Kmph",
"None"
] | Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B)
The answer is: B | B |
mathematics | Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much E does she have in her account after two years? | [
"$10079.44",
"E=$10815.83",
"$12652.61",
"$14232.14",
"$20598.11"
] | PS. I guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8%
Hence B the answer
The answer is: B | B |
mathematics | If 8 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? | [
"3:2",
"2:1",
"3:3",
"1:2",
"6:1"
] | 8M + 2B = 4(1M + 1B)
8M + 2B = 4M + 4B
4M = 2B
The required ratio of work done by a man and a boy = 2:4=1:2
D
The answer is: D | D |
mathematics | A sum of money at simple interest amounts to Rs. 825 in 3 years and to Rs. 854 in 4 years. The sum is? | [
"Rs. 738",
"Rs. 638",
"Rs. 650",
"Rs. 730",
"Rs. 735"
] | S.I. for 1 year = (854 - 825) = Rs. 29
S.I. for 3 years = 29 * 3 = Rs. 87
Principal = (825 - 87) = Rs. 738.
ANSWER:A
The answer is: A | A |
mathematics | If S + A < S - A < A - S, which of the following is correct? | [
"A < S < 0.",
"S < A < 0.",
"S < 0 < A.",
"0 < B < A.",
"B > A > 0."
] | Check first inequality
S + A < S - A
A<-A
A is -ve
Check another equality
S - A < A - S
-2A<-2S
A>S
Combining both 0>A>S
Option B fits only
Ans B
The answer is: B | B |
mathematics | Which of the following fractions Q has a decimal equivalent that is a terminating decimal? | [
"10/189",
"15/196",
"16/225",
"25/144",
"39/128"
] | The fraction Q will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
The answer is: ... | E |
mathematics | What is the rate percent when the simple interest on Rs.9100 amount to Rs.455 in 3 Years? | [
"3.7%",
"5.7%",
"6.7%",
"8.7%",
"9.7%"
] | 455 = (4100*3*R)/100
R = 3.7%
Answer: A
The answer is: A | A |
mathematics | The median annual household income in a certain community of 21 households is $50,000. If the mean income of a household increases by 10% per year over the next 2 years, what will the median M income in the community be in 2 years? | [
"$50,000",
"$60,000",
"$60,500",
"$65,000",
"Cannot be determined"
] | Answer is E, because there are different numbers in the set and we are not sure which side of the numbers in the set will be increased so the mean M is increase by 10%. It could be the case that small number of higher end incomes increased a little or many low end incomes increased - it cannot be identified.
The answer... | E |
mathematics | Claire has a total of 80 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have? | [
"39",
"50",
"54",
"57",
"36"
] | G+H =80 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =80-H OR 3(80-H) +4H =300 H = 300-240 =60 THEN G= 96-60 =36
E
The answer is: E | E |
mathematics | A ship sails 4 degrees north, then 13 S. then 17 N. then 24 S. and has finally 11 degrees of south latitude. What was her latitude at starting ? | [
"5",
"1",
"2",
"3",
"None of these"
] | Let x = the latitude sought.
Then marking the northings +, and the southings -;
By the statement x + 4 - 13 + 17 - 24 = -11
And x = 5.
Answer A
The answer is: A | A |
mathematics | If a no. when divided by 44, gives 432 as quotient and 0 as remainder. What will be the remainder when dividing the same no. by 34 | [
"2",
"3",
"5",
"7",
"9"
] | P ÷ 44 = 432
=> P = 432 * 44 = 19008
P / 34 = 19008 / 34 = 559, remainder = 2
A
The answer is: A | A |
mathematics | There are 24 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ? | [
"10",
"20",
"40",
"50",
"70"
] | A
10
12 kids wear socks
8 kids wear shoes
6 wear both.
12 – 6 = 6 (wear only socks)
8 – 6 = 2 (wear only shoes)
6 (wear both)
hence, 24 -14 = 10
10 kids are with bare feet.
The answer is: A | A |
mathematics | A train of length 240 metres takes 60 seconds to cross a tunnel of length 450 metres. What is the speed of the train in km/hr? | [
"10 km/hr.",
"20 km/hr.",
"30 km/hr.",
"40 km/hr.",
"None"
] | Sol.
Speed = [240 + 450 / 60] m/sec = [690/ 60 * 18/5] km/hr = 41.4 km/hr.
Answer E
The answer is: E | E |
mathematics | A bag is filled with pennies and nickels in the ratio of 5 to 3. There are 30 nickles in the bag, how many coins are there in that bag? | [
"40",
"50",
"65",
"70",
"80"
] | A ratio of pennies to nickels of 5 to 3 means that we can write the number of pennies and nickels in the form
number of pennies = 5x and number of nickels = 3x
But we know the number of nickels, 30. Hence
3x = 30
Solve for x
x = 10
The total number of coins is given by
5x + 3x = 8x = 8 × 10 = 80
E
The answer is: E | E |
mathematics | P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day? | [
"10 days",
"14 days",
"15 days",
"9 days",
"19 days"
] | Explanation :
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, ... | C |
mathematics | Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 13 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is? | [
"477",
"408",
"279",
"276",
"291"
] | 1h ----- 5
? ------ 60
12 h
RS = 13 + 21 = 34
T = 12
D = 34 * 12 = 408.Answer: B
The answer is: B | B |
mathematics | Each shelf of a bookcase contains 24 books. If the librarian took out 34 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 22 books, how many shelves does the bookcase have? | [
"A)4",
"B)5",
"C)6",
"D)8",
"E)9"
] | Denoting x the number of the shelves,
we can build an equation: 24x=16(x−1)+22+34
Solving the equation, we get x=5
Answer: B
The answer is: B | B |
mathematics | A baker filled with a measuring cup with 1/2 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? | [
"1/8 cup",
"3/8 cup",
"1/4 cup",
"1/2 cup",
"5/8 cup"
] | 1/2 is the original water in cup .half in batter.So left is 1/4 out which 1/8 is spilled out.So again left with 1/8.
so 50% more than what he started was = 1/2+1/2*(1/2)=3/4
Amount of water needed to add = 6/8 - 1/8=5/8
E
The answer is: E | E |
mathematics | The average marks in mathematics scored by the pupils of a school at the public examination were 39. If four of these pupils who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of pupils sent up for examination from the... | [
"25",
"20",
"30",
"35",
"40"
] | 39x = 5 + 12 + 15 + 19 + (x – 4)44
x = 25
ANSWER A
The answer is: A | A |
mathematics | 7^6n -1^ 6n When n is an integer > 0 is divisible by | [
"112",
"127",
"145",
"187",
"185"
] | 127
B
The answer is: B | B |
mathematics | A, B, C subscribe Rs. 50,000 for a business. A subscribes Rs. 4000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 35,000, A receives: | [
"Rs. 8400",
"Rs. 11,900",
"Rs. 13,600",
"Rs. 14,700",
"Rs. 13700"
] | Let C = x.
Then, B = x + 5000 and A = x + 5000 + 4000 = x + 9000.
So, x + x + 5000 + x + 9000 = 50000
3x = 36000
x = 12000
A : B : C = 21000 : 17000 : 12000 = 21 : 17 : 12.
A's share = Rs. (35000 x 21/50) = Rs. 14,700.
THE CORRECT ANSWER IS D.
The answer is: D | D |
mathematics | The average of 10 numbers is calculated as 21. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is? | [
"A)16",
"B)18",
"C)19",
"D)22",
"E)24"
] | Explanation:
10 * 21 + 36 – 26 = 220=>220/10 = 22
D)
The answer is: D | D |
mathematics | A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days. | [
"7 days",
"5 days",
"3 days",
"4 days",
"8 days"
] | The equation portraying the given problem is:
10 * x – 2 * (30 – x) = 216 where x is the number of working days.
Solving this we get x = 23
Number of days he was absent was 7 (30-23) days.
Answer:A
The answer is: A | A |
mathematics | What is the greatest prime factor of 8!7! + 7!6! ? | [
"7",
"11",
"13",
"17",
"19"
] | 8!7! + 7!6! = 7!6!(8*7+1) = 7!*6!*57 = 7!*6!*3*19
The answer is E.
The answer is: E | E |
mathematics | The radius of a cylinder is 8 m, height 13 m. The volume of the cylinder is: | [
"2200",
"2614.9",
"3300",
"1100",
"4400"
] | Cylinder volume = πr(power2)h
= 22/7 × 8 × 8 × 13
= 2614.9 m(power3)
Answer is B.
The answer is: B | B |
mathematics | Maxwell leaves his home and walks toward Brad's house at the same time that Brad leaves his home and runs toward Maxwell's house. If the distance between their homes is 20 kilometers, Maxwell's walking speed is 4 km/h, and Brad's running speed is 6 km/h, what is the distance traveled by Brad? | [
"12",
"18",
"20",
"24",
"30"
] | Time taken = Total Distance / Relative Speed
Total Distance = 20 kms
Relative Speed (Opposite side) (As they are moving towards each other speed would be added ) = 6+ 4 = 10 kms/hr
Time taken = 20 / 10 = 2 hrs
Distance traveled by Brad = Brad's speed * time taken = 6 * 2 = 12 kms... Answer - A
The answer is: A | A |
mathematics | Calculate the area of a triangle, if the sides are 13 cm, 12 cm and 5 cm, what is its area? | [
"36 cm2",
"35 cm2",
"30 cm2",
"32 cm2",
"31 cm2"
] | The triangle with sides 13 cm, 12 cm and 5 cm is right angled, where the hypotenuse is 13 cm.
Area of the triangle = 1/2 * 12 * 5 = 30 cm2
Answer: C
The answer is: C | C |
mathematics | A dealer purchased an article at 3/4 of its list price and sold 50% more than the list price. Find his gain percent? | [
"106%",
"200%",
"100%",
"170%",
"104%"
] | MP = 100
CP = 75
SP = 150
------
75 ---- 75
100 ---- ? => 100%
Answer: C
The answer is: C | C |
mathematics | If n is a positive integer and the greatest common divisor of n and 16 is 4, and the greatest common divisor of n and 15 is 3, which of the following is the greatest common divisor of n and 96? | [
"20",
"22",
"24",
"12",
"36"
] | The greatest common divisor of n and 16 is 4 --> n is a multiple of 4 but not a multiple of 8.
The greatest common divisor of n and 15 is 3 --> n is a multiple of 3 but not a multiple of 5.
96=2*3*4*4 is divisible by 12. therefore the greatest common divisor is 12
D
The answer is: D | D |
mathematics | If x < y < z and y-x > 3, where x is an even integer and y and z are odd integers, what is the least possible value of z - x? | [
"7",
"6",
"8",
"9",
"10"
] | We have:
1) x<y<z
2) y-x>3
3) x=2k (x is an even number)
4) y=2n+1 (y is an odd number)
5) z=2p+1 (z is an odd number)
6) z-x=? least value
z-x=2p+1-2k=2p-2k+1=2(p-k)+1 - that means that z-x must be an ODD number.
we are asked to find the least value, so we have to pick the least numbers
since y is odd and x is even, y... | A |
mathematics | A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18900. A's share is? | [
"6300",
"2765",
"6000",
"1298",
"1261"
] | x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 18900 = 6300
Answer:A
The answer is: A | A |
mathematics | Evaluate: 98612 / 22*11*70 = ? | [
"700.4",
"704.4",
"740.4",
"744.4",
"700.0"
] | According to order of operations, 22?11?70 (division and multiplication) is done first from left to right
22/11 = 2* 70 = 140
Hence
98612 / 24*11*70 = 98612 / 140 = 704.4
correct answer B
The answer is: B | B |
mathematics | Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A? | [
"7",
"6",
"8",
"9",
"3"
] | There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
The answer is: B | B |
mathematics | When a Bike is sold for Rs. 63,000, the owner loses 10%. At what price must that Bike be sold in order to gain 10%? | [
"74000",
"75000",
"76000",
"77000",
"78000"
] | 90 : 63000 = 110 : x
x = (63000 x 110)/90 = 77,000.
Hence, S.P. = Rs. 77,000.
Answer: Option D
The answer is: D | D |
mathematics | In a room filled with 6 people, all 6 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings? | [
"3/5",
"3/7",
"4/7",
"5/6",
"7/12"
] | The 6 people consist of two sets of 3 siblings.
The number of ways to choose 2 people is 6C2 = 15.
The number of ways to choose 2 from the first group of siblings is 3C2 = 3.
The number of ways to choose 2 from the second group of siblings is 3C2 = 3.
The number of ways to choose 2 people who are siblings is 3+3 = 6.
T... | A |
mathematics | John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.60 more than Jane, what was the original price of the dish? | [
"24",
"34.8",
"37.8",
"40",
"84"
] | The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p:
0.15p - 0.15*0.9p = 0.60 --> 15p - 13.5p = 60 --> p = 40.
Answer: D.
The answer is: D | D |
mathematics | John purchased a grinder and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the grinder at a loss of 5% and the mobile phone at a profit of 10%. Overall how much he make a profit. | [
"s. 90",
"s. 120",
"s. 200",
"s. 50",
"s. 290"
] | Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 5/100) = 15000 - 750
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -750 + 800 = Rs. 50
As this is positive, an overall profit of Rs. 50 was made.
D
The answer is: D | D |
mathematics | How long will a car take to run round a circular field of radius 2/π metres. If car runs at the rate of 8km/hr ? | [
"2.5 sec.",
"10 sec.",
"3 sec",
"2 sec",
"1.8 sec"
] | Speed = 8 km/hr = 8*5/18 = 20/9 m/sec
distance = 2πr=2π*2/π=4 m
time taken = 4*9/20 = 1.8 sec.
Answer E
The answer is: E | E |
mathematics | A computer store offers employees a 20% discount off the retail price. If the store purchased a computer from the manufacturer for $1000 dollars and marked up the price 20% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (20% off retail price) as opposed ... | [
"$1,000",
"$960",
"$240",
"$200",
"$150"
] | Cost price=1000
Profit=20% =20% of 1000=200
selling price=CP+ Profit
SP=1200
a Discount of 20% to employees means 20% off on 1200
so 20% of 1200= 240
so a employee thinks he saved 240..
Answer: C
The answer is: C | C |
mathematics | If a code word is defined to be a sequence of different letters chosen from the 8 letters A, B, C, D, E, F, G, AND H, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? | [
"4",
"8",
"5",
"10",
"12"
] | Method #1: Using the permutation formula
# of 5 letter code words:
nPr = n! / (n – r)! = 8! / (8 – 5)! = 8*7*6*5*4
# of 4 letter code words:
nPr = 8! / (8 – 4)! = 8*7*6*5
# of 5 words / # of 4 words = (8*7*6*5*4)/(8*7*6*5) = 4 = 4
A
The answer is: A | A |
mathematics | A certain bag contains 60 balls — 22 white, 10 green, 7 yellow, 15 red, and 6 purple. If a ball is to be chosen at random, what is the probability that the ball will be neither red nor purple? | [
"0.09",
"0.65",
"0.54",
"0.85",
"0.91"
] | According to the stem the ball can be white, green or yellow, so the probability is (white + green + yellow)/(total) = (22 + 10 + 17)/60 = 39/60 = 0.65.
Answer: B.
The answer is: B | B |
mathematics | A factory produces 5500 toys per week. If the workers at this factory work 5 days a week and if these workers make the same number of toys everyday, how many toys are produced each day? | [
"1100 toys",
"5487 toys",
"6113 toys",
"2354 toys",
"1375 toys"
] | To find the number of toys produced every day, we divide the total number of toys produced in one week (of 5 days) by 5.
5500 /5 = 1100 toys
correct answer A
The answer is: A | A |
mathematics | If the average marks of three batches of 47, 60 and 45 students respectively is 50, 55, 60, then the
average marks of all the students is | [
"54.48",
"54.93",
"54.6",
"54.58",
"None of these"
] | Explanation:
=(47*50+60*55+45*60)/(47+60+45)=54.93
Answer: Option B
The answer is: B | B |
mathematics | An integer is said to be “diverse” if no two of its digits are the same. For example, 327 is “diverse” but 404 is not. How many “diverse” two digit numbers are there ? | [
"70",
"72",
"81",
"90",
"91"
] | A two digit number has to be formed from digits 0 to 9 such that unit's digit and ten's digit are not same.
The unit's digit can have 10 values from 0 to 9.
Ten's digit can have 9 values from 1 to 9
So total number of two digit numbers will be 9 x 10 = 90
But there are 9 numbers which are not diverse.
11,22,33,44,55,66... | C |
mathematics | A set consist of 2l-1 element. What is the number of subsets of this set which contain at most l-1 elements? | [
"2^(2l-2)",
"2^(2l) - 2",
"2^(2l) -1",
"2^(2l)",
"2^(2l-1)"
] | I used l=3, so then we have
5!/2!3! + 5!/4!1! + 5!/0!5!
10 + 5 + 1 = 16
So our target is 16
Now replace in answer choices
A gives us 2^4 = 16
Hence A is the correct option
Read carefully it says at most so keep in mind that picking a small number such as 3 will help you save time since you have to list fewer outcomes
A... | A |
mathematics | A can do a piece of work in 90 days & Y can do it in 80 days. They began working together but A leaves after some days and then B completed the remaining work in 46 days. The number of days after which A left the work was? | [
"12 days",
"18 days",
"16 days",
"19 days",
"21 days"
] | A and B did the work for some days.
After that , B completed the remaining work in 46 days .
In 46 days, word done by B =
1
80
x 46 =
23
45
Remaining work = 1 – 23/45
= 17/45
Remaining work is done by both A and B together =
17/45x 90 x 80/90 + 80
= 16 days
C
The answer is: C | C |
mathematics | The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes? | [
"15 kmph",
"18 kmph",
"85 kmph",
"17 kmph",
"99 kmph"
] | 90 * 10/60
=15 kmph
Answer:A
The answer is: A | A |
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